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## Asymptotics
Terms modified by Asymptotics ## Selected Abstracts## Asymptotic Back Strain Approach for Estimation of Effective Properties of Multiphase Materials ADVANCED ENGINEERING MATERIALS, Issue 1-2 2007A. GusevEstimation of the effective properties of composite materials from those of the constituents and the material's morphology is a classical problem of both theoretical and technological interest. In this work, the authors have introduced an asymptotic back strain finite element approach for numerical estimation of effective properties of multiphase materials. The proposed approach should open an appealing pathway to rational and effective computer aided design of random microstructure composite materials. [source] ## Gain functions for large herbivores: tests of alternative models JOURNAL OF ANIMAL ECOLOGY, Issue 1 2005KATE R. SEARLESummary 1The gain function describes the amount of food consumed in a patch as a function of patch residence time. Gain functions play a central role in foraging theory but alternative functional forms portraying dynamics of gain have not been evaluated. We evaluated the strength of evidence in the data for alternative gain functions of mule deer (Odocoileus hemionus, Rafinesque 1817) and blue duikers (Cephalophus monticola, Blythe 1848) feeding in patches composed of different plant species and plant sizes. 2Gain functions decelerated with patch residence time, but there was considerable variation among individual animals and patch types in the nature of this response. Asymptotic and piecewise-linear models received the greatest support in the data. 3Deceleration in gain was caused by a composite of effects that retarded instantaneous intake rate, including reductions in bite mass and increases in bite interval (time between successive bites). Bite interval increased as a result of increases in processing time of accumulated forage in the mouth, rather than increases in time allocated to cropping. 4We demonstrated that unwarranted assumptions about the shape of gain functions can have profound effects on predictions of patch models. Predictions of the classical patch model using purely asymptotic gain functions contrasted sharply with predictions of model-averaged gain functions that were supported by the data. [source] ## The complex Bingham quartic distribution and shape analysis JOURNAL OF THE ROYAL STATISTICAL SOCIETY: SERIES B (STATISTICAL METHODOLOGY), Issue 5 2006J. T. KentSummary., The complex Bingham distribution was introduced by Kent as a tractable model for landmark-based shape analysis. It forms an exponential family with a sufficient statistic which is quadratic in the data. However, the distribution has too much symmetry to be widely useful. In particular, under high concentration it behaves asymptotically as a normal distribution, but where the covariance matrix is constrained to have complex symmetry. To overcome this limitation and to provide a full range of asymptotic normal behaviour, we introduce a new ,complex Bingham quartic distribution' by adding a selection of quartic terms to the log-density. In the simplest case this new distribution corresponds to Kent's FB5 -distribution. Asymptotic and saddlepoint methods are developed for the normalizing constant to facilitate maximum likelihood estimation. Examples are given to show the usefulness of this new distribution. [source] ## Generation of Gevrey class semigroup by non-selfadjoint Euler,Bernoulli beam model MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 18 2006Marianna A. ShubovAbstract Asymptotic and spectral properties of a non-selfadjoint operator that is a dynamics generator for the Euler,Bernoulli beam model of a finite length are studied in this paper. The hyperbolic equation, which governs the vibrations of the Euler,Bernoulli beam model, is supplied with a one-parameter family of physically meaningful boundary conditions containing damping terms. The initial boundary-value problem is equivalent to the evolution equation that generates a strongly continuous semigroup in the state space of the system. It is found that the semigroup, being non-analytic, belongs to Gevrey class semigroups. This means that the differentiability of such semigroup is slightly weaker than that of an analytic semigroup. In the forthcoming works, the results of the present paper will be applied (a) to the solution of the exact controllability problem for Euler,Bernoulli beam and (b) to spectral analysis of a planar network of serially connected Euler,Bernoulli beams modelling ,flying wing configurations' in aeronautic engineering. Copyright © 2006 John Wiley & Sons, Ltd. [source] ## Asymptotic and spectral properties of operator-valued functions generated by aircraft wing model MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 3 2004A. V. BalakrishnanAbstract The present paper is devoted to the asymptotic and spectral analysis of an aircraft wing model in a subsonic air flow. The model is governed by a system of two coupled integro-differential equations and a two parameter family of boundary conditions modelling the action of the self-straining actuators. The differential parts of the above equations form a coupled linear hyperbolic system; the integral parts are of the convolution type. The system of equations of motion is equivalent to a single operator evolution,convolution equation in the energy space. The Laplace transform of the solution of this equation can be represented in terms of the so-called generalized resolvent operator, which is an operator-valued function of the spectral parameter. More precisely, the generalized resolvent is a finite-meromorphic function on the complex plane having a branch-cut along the negative real semi-axis. Its poles are precisely the aeroelastic modes and the residues at these poles are the projectors on the generalized eigenspaces. The dynamics generator of the differential part of the system has been systematically studied in a series of works by the second author. This generator is a non-selfadjoint operator in the energy space with a purely discrete spectrum. In the aforementioned series of papers, it has been shown that the set of aeroelastic modes is asymptotically close to the spectrum of the dynamics generator, that this spectrum consists of two branches, and a precise spectral asymptotics with respect to the eigenvalue number has been derived. The asymptotical approximations for the mode shapes have also been obtained. It has also been proven that the set of the generalized eigenvectors of the dynamics generator forms a Riesz basis in the energy space. In the present paper, we consider the entire integro-differential system which governs the model. Namely, we investigate the properties of the integral convolution-type part of the original system. We show, in particular, that the set of poles of the adjoint generalized resolvent is asymptotically close to the discrete spectrum of the operator that is adjoint to the dynamics generator corresponding to the differential part. The results of this paper will be important for the reconstruction of the solution of the original initial boundary-value problem from its Laplace transform and for the analysis of the flutter phenomenon in the forthcoming work. Copyright © 2004 John Wiley & Sons, Ltd. [source] ## Asymptotic and spectral analysis of non-selfadjoint operators generated by a filament model with a critical value of a boundary parameter MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 3 2003Marianna A. ShubovAbstract We consider a class of non-selfadjoint operators generated by the equation and the boundary conditions, which govern small vibrations of an ideal filament with non-conservative boundary conditions at one end and a heavy load at the other end. The filament has a non-constant density and is subject to a viscous damping with a non-constant damping coefficient. The boundary conditions contain two arbitrary complex parameters. In our previous paper (Mathematical Methods in the Applied Sciences 2001; 24(15) : 1139,1169), we have derived the asymptotic approximations for the eigenvalues and eigenfunctions of the aforementioned non-selfadjoint operators when the boundary parameters were arbitrary complex numbers except for one specific value of one of the parameters. We call this value the critical value of the boundary parameter. It has been shown (in Mathematical Methods in the Applied Sciences 2001; 24(15) : 1139,1169) that the entire set of the eigenvalues is located in a strip parallel to the real axis. The latter property is crucial for the proof of the fact that the set of the root vectors of the operator forms a Riesz basis in the state space of the system. In the present paper, we derive the asymptotics of the spectrum exactly in the case of the critical value of the boundary parameter. We show that in this case, the asymptotics of the eigenvalues is totally different, i.e. both the imaginary and real parts of eigenvalues tend to ,as the number of an eigenvalue increases. We will show in our next paper, that as an indirect consequence of such a behaviour of the eigenvalues, the set of the root vectors of the corresponding operator is not uniformly minimal (let alone the Riesz basis property). Copyright © 2003 John Wiley & Sons, Ltd. [source] ## A CLASS OF MODELS DESCRIBING AGE STRUCTURE DYNAMICS IN A NATURAL FOREST NATURAL RESOURCE MODELING, Issue 2 2002MICHAEL A. KRAEMERABSTRACT. The age dynamics of a natural forest is modeled by the von-Foerster partial differential equation for the age density, while the seedling density is obtained as a solution of an integro-differential equation. This seedling density equation contains a small parameter, the ratio of seedling re-establishment time and the life span of an average tree in the forest. Several models are introduced that take into account various mortality curves and growth functions of trees, the dependence of seedlings carrying capacity on forest size, and different types of seedlings re-establishment. Asymptotic, analytic and numerical methods are used to solve typical example problems. [source] ## Generalized Spitzer Function with Finite Collisionality in Toroidal Plasmas CONTRIBUTIONS TO PLASMA PHYSICS, Issue 8 2010W. KernbichlerAbstract The drift kinetic equation solver NEO-2 [1] which is based on the field line integration technique has been applied to compute the generalized Spitzer function in a tokamak with finite plasma collisionality. The resulting generalized Spitzer function has specific features which are pertinent to the finite plasma collisionality. They are absent in asymptotic (collisionless or highly collisional) regimes or in results drawn from interpolation between asymptotic limits. These features have the potential to improve the overall ECCD efficiency if one optimizes the microwave beam launch scenarii accordingly (© 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] ## Big Consequences of Small Changes (Non-locality and non-linearity of Hartree-Fock equations) CONTRIBUTIONS TO PLASMA PHYSICS, Issue 7-8 2009M.Ya. AmusiaAbstract It is demonstrated that non-locality and non-linearity of Hartree-Fock equations dramatically affect the properties of their solutions that essentially differ from solutions of Schrödinger equation with a local potential. Namely, it acquires extra zeroes, has different coordinate asymptotic, violates so-called gauge-invariance, has different scattering phases at zero energy, has in some cases several solutions with the same set of quantum numbers, usually equivalent expressions of current and Green's functions became non-equivalent. These features result in a number of consequences for probabilities of some physical processes, leading e. g. to extra width of atomic Giant resonances and enhance considerably the ionization probability of inner atomic electrons by a strong field (© 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] ## The influence of arbuscular mycorrhizae on the relationship between plant diversity and productivity ECOLOGY LETTERS, Issue 2 2000John N KlironomosEcological theory predicts a positive and asymptotic relationship between plant diversity and ecosystem productivity based on the ability of more diverse plant communities to use limiting resources more fully. This is supported by recent empirical evidence. Additionally, in natural ecosystems, plant productivity is often a function of the presence and composition of mycorrhizal associations. Yet, the effect of mycorrhizal fungi on the relationship between plant diversity and productivity has not been investigated. We predict that in the presence of AMF, productivity will saturate at lower levels of species richness because AMF increase the ability of plant species to utilize nutrient resources. In this study we manipulated old-field plant species richness in the presence and absence of two species of AMF. We found that in the absence of AMF, the relationship between plant species richness and productivity is positive and linear. However, in the presence of AMF, the relationship is positive but asymptotic, even though the maximum plant biomass was significantly different between the two AMF treatments. This is consistent with the hypothesis that AMF increase the redundancy of plant species in the productivity of plant communities, and indicates that these symbionts must be considered in future investigations of plant biodiversity and ecosystem function. [source] ## Testing Parameters in GMM Without Assuming that They Are Identified ECONOMETRICA, Issue 4 2005Frank KleibergenWe propose a generalized method of moments (GMM) Lagrange multiplier statistic, i.e., the K statistic, that uses a Jacobian estimator based on the continuous updating estimator that is asymptotically uncorrelated with the sample average of the moments. Its asymptotic ,2 distribution therefore holds under a wider set of circumstances, like weak instruments, than the standard full rank case for the expected Jacobian under which the asymptotic ,2 distributions of the traditional statistics are valid. The behavior of the K statistic can be spurious around inflection points and maxima of the objective function. This inadequacy is overcome by combining the K statistic with a statistic that tests the validity of the moment equations and by an extension of Moreira's (2003) conditional likelihood ratio statistic toward GMM. We conduct a power comparison to test for the risk aversion parameter in a stochastic discount factor model and construct its confidence set for observed consumption growth and asset return series. [source] ## Measuring natural abundance of 13C in respired CO2: variability and implications for non-invasive dietary analysis FUNCTIONAL ECOLOGY, Issue 6 2001S. E. PERKINSSummary 1,Three experiments were performed, using laboratory mice (Mus musculus) as a model species, to evaluate the potential of using measurements of carbon isotope ratios in expired CO2 for tracing diets. 2,Breath 13C signatures of mice fed a constant diet (,21·4, ± 0·35) reflected their diet, but were depleted by on average ,5·7,. Body mass, sex and age were independent and significant factors correlated with the variability of 13C enrichment in respired CO2. 3,Breath 13C signatures from starved mice (7 h) were lower than unstarved mice by 2·0,. Subsequently when starved mice were fed a small meal of a new diet, breath 13C signatures approached those of the new diets within 15 min, returning to preingestion levels after 105 min. 4,After a permanent diet switch 13C values of breath were not asymptotic within 6 days, possibly because of use of fat reserves during the daytime carrying an isotopic memory of the previous diet. Hence, individual breath 13C signatures may vary according to nutritive state and previous dietary history. 5,Interindividual variability was measured at 3·3,. The implications are that large samples of individuals will be required to distinguish between diets of different populations where the isotopic difference between their diets was small , for example, that expected between herbivorous and carnivorous diets. However, breath would be suitable for distinguishing between dietary intakes of individuals for food types that are isotopically more distinct , such as between C3 and C4 plants. [source] ## Extension of weakly compressible approximations to incompressible thermal flows INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 1 2008Mofdi El-AmraniAbstract Weakly compressible and advection approximations of incompressible isothermal flows were developed and tested in (Commun. Numer. Methods Eng. 2006; 22:831,847). In this paper, we extend the method to solve equations governing incompressible thermal flows. The emphasis is again on the reconstruction of unconditionally stable numerical scheme such that, restriction on time steps, projection procedures, solution of linear system of algebraic equations and staggered grids are completely avoided in its implementation. These features are achieved by combining a low-Mach asymptotic in compressible flow equations with a semi-Lagrangian method for the weakly compressible approach. The time integration is carried out using an explicit Runge,Kutta with variable stages. The method is applied to the natural convection flows in a squared cavity for both steady and transient computations. The numerical results demonstrate high resolution of the proposed method and confirm its capability to provide accurate and efficient simulations for thermal flow problems. Copyright © 2006 John Wiley & Sons, Ltd. [source] ## A note on enrichment functions for modelling crack nucleation INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 12 2003J. BellecAbstract For particular discretizations and crack configurations, the enhanced approximations of the eXtended finite-element method (X-FEM) cannot accurately represent the discontinuities in the near-tip displacement fields. In this note, we focus on the particular case where the extent of the crack approaches the support size of the nodal shape functions. Under these circumstances, the asymptotic ,branch' functions for each tip may extend beyond the length of the crack, resulting in a non-conforming approximation. We explain the limitations of the standard approximation for arbitrary discontinuities, and propose a set of adjustments to remedy the deficiencies. We also provide numerical results that demonstrate the advantages of the modified approximation. Copyright © 2003 John Wiley & Sons, Ltd. [source] ## On the spectrum of the electric field integral equation and the convergence of the moment method INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 1 2001Karl F. WarnickAbstract Existing convergence estimates for numerical scattering methods based on boundary integral equations are asymptotic in the limit of vanishing discretization length, and break down as the electrical size of the problem grows. In order to analyse the efficiency and accuracy of numerical methods for the large scattering problems of interest in computational electromagnetics, we study the spectrum of the electric field integral equation (EFIE) for an infinite, conducting strip for both the TM (weakly singular kernel) and TE polarizations (hypersingular kernel). Due to the self-coupling of surface wave modes, the condition number of the discretized integral equation increases as the square root of the electrical size of the strip for both polarizations. From the spectrum of the EFIE, the solution error introduced by discretization of the integral equation can also be estimated. Away from the edge singularities of the solution, the error is second order in the discretization length for low-order bases with exact integration of matrix elements, and is first order if an approximate quadrature rule is employed. Comparison with numerical results demonstrates the validity of these condition number and solution error estimates. The spectral theory offers insights into the behaviour of numerical methods commonly observed in computational electromagnetics. Copyright © 2001 John Wiley & Sons, Ltd. [source] ## Modelling and simulation of fires in vehicle tunnels INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 3 2004I. GasserAbstract Applying a low-Mach asymptotic for the compressible Navier,Stokes equations, we derive a new fluid dynamics model,which should be capable to model large temperature differences in combination with the low-Mach number limit. The model is used to simulate fires in vehicle tunnels, where the standard Boussinesq-approximation for the incompressible Navier,Stokes seems to be inappropriate due to the high temperatures developing in the tunnel. The model is implemented using a modified finite-difference approach for the incompressible Navier,Stokes equations and tested in some realistic fire events. Copyright © 2004 John Wiley & Sons, Ltd. [source] ## Further constructive results on interconnection and damping assignment control of mechanical systems: the Acrobot example INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 14 2006Arun D. MahindrakarAbstract Interconnection and damping assignment passivity-based control is a controller design methodology that achieves (asymptotic) stabilization of mechanical systems endowing the closed-loop system with a Hamiltonian structure with a desired energy function,that qualifies as Lyapunov function for the desired equilibrium. The assignable energy functions are characterized by a set of partial differential equations that must be solved to determine the control law. A class of underactuation degree one systems for which the partial differential equations can be explicitly solved,making the procedure truly constructive,was recently reported by the authors. In this brief note, largely motivated by the interesting Acrobot example, we pursue this investigation for two degrees-of-freedom systems where a constant inertia matrix can be assigned. We concentrate then our attention on potential energy shaping and give conditions under which an explicit solution of the associated partial differential equation can be obtained. Using these results we show that it is possible to swing-up the Acrobot from some configuration positions in the lower half plane, provided some conditions on the robot parameters are satisfied. Copyright © 2006 John Wiley & Sons, Ltd. [source] ## Adaptive output feedback tracking control of spacecraft formation INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 2-3 2002Hong WongAbstract In this paper, an adaptive, output feedback control design methodology is presented for a spacecraft formation flying (SFF) system. A Lagrangian derivation of the SFF model is considered to produce position dynamics for follower spacecraft #n relative to follower spacecraft #(n,1), where n is an arbitrary positive integer, assuming that the leader spacecraft in the formation follows a no-thrust, natural, elliptical orbit. Next, a control law is designed to provide a filtered velocity measurement and a desired adaptive compensation with semi-global, asymptotic, relative position tracking. To show the efficacy of the control algorithm, all desired trajectories are generated online by numerically solving the unperturbed nonlinear SFF dynamics with initial conditions satisfying a no-thrust, natural orbit constraint equation. The proposed control law is simulated for the case of two and three spacecraft and is shown to yield semi-global, asymptotic tracking of the relative position in addition to the convergence of disturbance parameter estimates. Copyright © 2002 John Wiley & Sons, Ltd. [source] ## Age-based life history parameters and status assessments of by-catch species (Lethrinus borbonicus, Lethrinus microdon, Pomacanthus maculosus and Scolopsis taeniatus) in the southern Arabian Gulf JOURNAL OF APPLIED ICHTHYOLOGY, Issue 3 2010E. GrandcourtSummary Life history and demographic parameters for Lethrinus borbonicus, Lethrinus microdon, Pomacanthus maculosus and Scolopsis taeniatus in the southern Arabian Gulf were estimated using a combination of size frequency, biological and size-at-age data. Defined structural increments consisting of alternating translucent and opaque bands in transverse sections of sagittal otoliths were validated as annuli. The maximum age estimates ranged from 5 years for Scolopsis taeniatus to 36 years for Pomacanthus maculosus. The size-at-age relationships were highly asymptotic in form with the majority of growth being achieved early in life. There were significant differences in the growth characteristics between sexes for Pomacanthus maculosus, with males approaching a larger asymptotic size at a faster rate than females. With the exception of Scolopsis taeniatus, the mean age at which fish became vulnerable to capture was lower than the mean age at first sexual maturity. The stocks of L. microdon, P. maculosus and S. taeniatus were exploited within sustainable limits, conversely, L. borbonicus was found to be overexploited and recruitment overfishing may have occurred as the relative spawner biomass per recruit was below 30% of the unexploited state. [source] ## Temporal patterns of growth in larval cohorts of the Japanese sardine Sardinops melanostictus in a coastal nursery area JOURNAL OF FISH BIOLOGY, Issue 6 2008G. PlazaGrowth patterns of larval sardine Sardinops melanostictus were studied in a coastal nursery area, in southern Japan for four monthly hatch cohorts of larvae (November, December, January and February) for the 2003,2004 and 2004,2005 seasons. Laird,Gompertz models were fitted to each cohort using both total length (LT)-at-age at capture and mean LT -at-age data derived from backcalculations. In both approaches, the absolute daily growth rates (GR) and absolute daily growth rates at the inflection point (GXO) were estimated. In parallel, individual growth rates (GI) were derived from backcalculated LT (LB). Growth showed the following general common patterns irrespective of hatch month, season and methods: (1) significant Laird,Gompertz fits, (2) asymptotic growth, (3) a decrease in GR after the inflexion point, except for February for the 2003,2004 season that showed an apparent constant growth pattern, (4) six in eight cohorts showed GXO ranging from 0·8 to 1·2 mm day,1 and (5) a decreasing tendency of GI from 1·75 to 0·24 mm day,1, from first feeding through the first month of larval life. The contrasting pattern between the 2003,2004 and the 2004,2005 seasons were: (1) allometric v. logarithmic (ln) LT and otolith radius relationships, (2) low GXOv. high GXO, (3) high GRv. low GR when growth turned asymptotic, (4) low GXOv. high GXO when monthly hatch cohorts were combined and (5) LB and GI not differing among monthly hatch cohorts. The differences in growth patterns and growth rates between seasons seemed to be linked to the influx of warmer and oligotrophic waters of the Kuroshio Current that triggered an increase of 3° C in the coastal area for the 2003,2004 seasons. In the overall context, however, the high GXO, within cohorts and seasons reported in the current study, suggests that either sea surface temperature (SST) or food availability, or both are in the optimal range of preferences for S. melanostictus larvae. Consequently, nearshore coastal areas seem to be playing an important role as a nursery area for the larval stage of this species. [source] ## On variable bandwidth selection in local polynomial regression JOURNAL OF THE ROYAL STATISTICAL SOCIETY: SERIES B (STATISTICAL METHODOLOGY), Issue 3 2000Kjell DoksumThe performances of data-driven bandwidth selection procedures in local polynomial regression are investigated by using asymptotic methods and simulation. The bandwidth selection procedures considered are based on minimizing ,prelimit' approximations to the (conditional) mean-squared error (MSE) when the MSE is considered as a function of the bandwidth h. We first consider approximations to the MSE that are based on Taylor expansions around h=0 of the bias part of the MSE. These approximations lead to estimators of the MSE that are accurate only for small bandwidths h. We also consider a bias estimator which instead of using small h approximations to bias naïvely estimates bias as the difference of two local polynomial estimators of different order and we show that this estimator performs well only for moderate to large h. We next define a hybrid bias estimator which equals the Taylor-expansion-based estimator for small h and the difference estimator for moderate to large h. We find that the MSE estimator based on this hybrid bias estimator leads to a bandwidth selection procedure with good asymptotic and, for our Monte Carlo examples, finite sample properties. [source] ## Asymptotic and spectral properties of operator-valued functions generated by aircraft wing model MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 3 2004A. V. BalakrishnanAbstract The present paper is devoted to the asymptotic and spectral analysis of an aircraft wing model in a subsonic air flow. The model is governed by a system of two coupled integro-differential equations and a two parameter family of boundary conditions modelling the action of the self-straining actuators. The differential parts of the above equations form a coupled linear hyperbolic system; the integral parts are of the convolution type. The system of equations of motion is equivalent to a single operator evolution,convolution equation in the energy space. The Laplace transform of the solution of this equation can be represented in terms of the so-called generalized resolvent operator, which is an operator-valued function of the spectral parameter. More precisely, the generalized resolvent is a finite-meromorphic function on the complex plane having a branch-cut along the negative real semi-axis. Its poles are precisely the aeroelastic modes and the residues at these poles are the projectors on the generalized eigenspaces. The dynamics generator of the differential part of the system has been systematically studied in a series of works by the second author. This generator is a non-selfadjoint operator in the energy space with a purely discrete spectrum. In the aforementioned series of papers, it has been shown that the set of aeroelastic modes is asymptotically close to the spectrum of the dynamics generator, that this spectrum consists of two branches, and a precise spectral asymptotics with respect to the eigenvalue number has been derived. The asymptotical approximations for the mode shapes have also been obtained. It has also been proven that the set of the generalized eigenvectors of the dynamics generator forms a Riesz basis in the energy space. In the present paper, we consider the entire integro-differential system which governs the model. Namely, we investigate the properties of the integral convolution-type part of the original system. We show, in particular, that the set of poles of the adjoint generalized resolvent is asymptotically close to the discrete spectrum of the operator that is adjoint to the dynamics generator corresponding to the differential part. The results of this paper will be important for the reconstruction of the solution of the original initial boundary-value problem from its Laplace transform and for the analysis of the flutter phenomenon in the forthcoming work. Copyright © 2004 John Wiley & Sons, Ltd. [source] ## Modeling and Simulation of Fires in Vehicle Tunnels PROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2003I. Teleaga M.Sc.Starting with compressible Navier-Stokes equations we derive a new fluid model by applying a low-Mach number asymptotic. The model is used to simulate fire events in vehicular tunnels. [source] ## Asymptotic evaluation of effective complex moduli of fibre-reinforced viscoelastic composite materials PROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2003I. Andrianov Prof. Dr. Sc.We propose an asymptotic approach for the evaluation of effective complex moduli of viscoelastic fibre-reinforced composite materials. Our method is based on the homogenization technique. We start with a non-trivial expansion of the input plane-strain boundary value problem by ratios of visco-elastic constants. This allows to simplify the governing equations to forms analogous to the complex transport problem. Then we apply the asymptotic homogenization method, coming from the original problem on multi-connected domain to the cell problem, defined on a unit cell of the periodic structure. For the analytical solution of the cell problem we apply the boundary perturbation technique, the asymptotic expansion by a distance between two neighbouring fibres and the method of two-point Padé approximants. As results we derive uniform analytical representations for effective complex moduli, valid for all values of the components volume fractions and properties. [source] ## Weight of a link in a shortest path tree and the Dedekind Eta function RANDOM STRUCTURES AND ALGORITHMS, Issue 3 2010Piet Van MieghemAbstract The weight of a randomly chosen link in the shortest path tree on the complete graph with exponential i.i.d. link weights is studied. The corresponding exact probability generating function and the asymptotic law are derived. As a remarkable coincidence, this asymptotic law is precisely the same as the distribution of the cost of one "job" in the random assignment problem. We also show that the asymptotic (scaled) maximum interattachment time to that shortest path tree, which is a uniform recursive tree, equals the square of the Dedekind Eta function, a central function in modular forms, elliptic functions, and the theory of partitions. © 2010 Wiley Periodicals, Inc. Random Struct. Alg., 2010 [source] ## The height of increasing trees RANDOM STRUCTURES AND ALGORITHMS, Issue 4 2008N. BroutinAbstract We extend results about heights of random trees (Devroye, JACM 33 (1986) 489,498, SIAM J COMP 28 (1998) 409,432). In this paper, a general split tree model is considered in which the normalized subtree sizes of nodes converge in distribution. The height of these trees is shown to be in probability asymptotic to clog n for some constant c. We apply our results to obtain a law of large numbers for the height of all polynomial varieties of increasing trees (Bergeron et al. Lect Notes Comput Sci (1992) 24,48).© 2008 Wiley Periodicals, Inc. Random Struct. Alg., 2008 [source] ## Largest planar matching in random bipartite graphs RANDOM STRUCTURES AND ALGORITHMS, Issue 2 2002Marcos KiwiAbstract For a distribution ,, over labeled bipartite (multi) graphs G = (W, M, E), |W| = |M| = n, let L(n) denote the size of the largest planar matching of G (here W and M are posets drawn on the plane as two ordered rows of nodes and edges are drawn as straight lines). We study the asymptotic (in n) behavior of L(n) for different distributions ,,. Two interesting instances of this problem are Ulam's longest increasing subsequence problem and the longest common subsequence problem. We focus on the case where ,, is the uniform distribution over the k -regular bipartite graphs on W and M. For k = o(n1/4), we establish that tends to 2 in probability when n , ,. Convergence in mean is also studied. Furthermore, we show that if each of the n2 possible edges between W and M are chosen independently with probability 0 < p < 1, then L(n)/n tends to a constant ,p in probability and in mean when n , ,. © 2002 Wiley Periodicals, Inc. Random Struct. Alg., 21: 162,181, 2002 [source] ## On quasi-likelihood inference in generalized linear mixed models with two components of dispersion THE CANADIAN JOURNAL OF STATISTICS, Issue 4 2003Brajendra C. SutradharAbstract The authors propose a quasi-likelihood approach analogous to two-way analysis of variance for the estimation of the parameters of generalized linear mixed models with two components of dispersion. They discuss both the asymptotic and small-sample behaviour of their estimators, and illustrate their use with salamander mating data. Les auteurs s'inspirent de l'analyse de la variance à deux voies pour proposer une méthode d'estimation de type quasi-vraisemblance des paramètres de modèles linéaires généralisés mixtes ayant deux composantes de dispersion. Es étudient le comportement asymptotique et à taille finie de leurs estimateurs et en illustrent l'emploi au moyen de données portant sur l'accouplement de salamandres. [source] ## Efficient Calculation of P-value and Power for Quadratic Form Statistics in Multilocus Association Testing ANNALS OF HUMAN GENETICS, Issue 3 2010Liping TongSummary We address the asymptotic and approximate distributions of a large class of test statistics with quadratic forms used in association studies. The statistics of interest take the general form D=XTA X, where A is a general similarity matrix which may or may not be positive semi-definite, and X follows the multivariate normal distribution with mean , and variance matrix ,, where , may or may not be singular. We show that D can be written as a linear combination of independent ,2 random variables with a shift. Furthermore, its distribution can be approximated by a ,2 or the difference of two ,2 distributions. In the setting of association testing, our methods are especially useful in two situations. First, when the required significance level is much smaller than 0.05 such as in a genome scan, the estimation of p-values using permutation procedures can be challenging. Second, when an EM algorithm is required to infer haplotype frequencies from un-phased genotype data, the computation can be intensive for a permutation procedure. In either situation, an efficient and accurate estimation procedure would be useful. Our method can be applied to any quadratic form statistic and therefore should be of general interest. [source] ## Marginal Analysis of Incomplete Longitudinal Binary Data: A Cautionary Note on LOCF Imputation BIOMETRICS, Issue 3 2004Richard J. CookSummary In recent years there has been considerable research devoted to the development of methods for the analysis of incomplete data in longitudinal studies. Despite these advances, the methods used in practice have changed relatively little, particularly in the reporting of pharmaceutical trials. In this setting, perhaps the most widely adopted strategy for dealing with incomplete longitudinal data is imputation by the "last observation carried forward" (LOCF) approach, in which values for missing responses are imputed using observations from the most recently completed assessment. We examine the asymptotic and empirical bias, the empirical type I error rate, and the empirical coverage probability associated with estimators and tests of treatment effect based on the LOCF imputation strategy. We consider a setting involving longitudinal binary data with longitudinal analyses based on generalized estimating equations, and an analysis based simply on the response at the end of the scheduled follow-up. We find that for both of these approaches, imputation by LOCF can lead to substantial biases in estimators of treatment effects, the type I error rates of associated tests can be greatly inflated, and the coverage probability can be far from the nominal level. Alternative analyses based on all available data lead to estimators with comparatively small bias, and inverse probability weighted analyses yield consistent estimators subject to correct specification of the missing data process. We illustrate the differences between various methods of dealing with drop-outs using data from a study of smoking behavior. [source] |